Effects of fire history on species richness and carbon stocks in a Peruvian puna grassland, and development of allometric equations for biomass estimation of common puna species
Maarten van der Eynden
Department of Ecology and Natural Resource Management Master Thesis 60 credits 2011
Effects of fire history on species richness and carbon stocks in a Peruvian puna grassland, and development of allometric equations
for biomass estimation of common puna species
Master of Science Thesis by Maarten van der Eynden
Supervisors:
Torbjørn Haugaasen – Department of Ecology and Natural Resource Management, UMB.
Imma Oliveras – Environmental Change Institute, University of Oxford.
Department of Ecology and Natural Resource Management
Norwegian University of Life Sciences (UMB) 11.05.11
I
Preface
This study was done as part of a project led by the University of Oxfords Environmental Change Institute investigating “The dynamics and carbon implications of fires in the Andes”. Field work was carried out near the Wayqecha research station near the city of Cusco, Peru. The thesis was written at the Department of Ecology and Natural Resource Management at the Norwegian University of Life Sciences (UMB). Thanks to the Department of Ecology and Natural Resource Management at UMB, Lånekassen and Andreas og K. Ludvig Endresens Legat for funding the project.
I would like to take this opportunity to sincerely thank my two wonderfully helpful and patient supervisors. Thank you both for exchanging e-mail addresses when you met at a conference some years ago and thereby setting the stage for what at least I have found a very rewarding cooperation between the three of us. Thank you Torbjørn for honest comments and an always encouraging attitude. Thank you Imma for excellent guidance in the field, and for always
keeping my spirit high, even when our samples went up in flames and fire research seemed like a very, very bad idea to an inexperienced Msc student.
I would also like to thank all the wonderful people who helped out with the fieldwork. Carlos Menor, Flor Zamora, Nelson Cahuana, Guissela Romani, Efrain Choque, Sandra Almeyda, Jose Kala, Jose Antonio and Walter Huaraca Huasco were all essential for the completion of this project. Thanks also to Matt Swan, Tim Hoolahan and all other students, researchers and staff I met in Cusco and Wayqecha. You all made this an unforgettable experience, filled with
interesting conversations, music, dance and many breathtaking attacks of laughter.
Finally, I would like to thank my wonderful girlfriend Oda, my family and my friends. Thank you for all the good times along the way, and for always supporting me, although I seriously doubt that you have any idea about what I was really doing, measuring all that grass in Peru.
II
III
Abstract
High-elevation ecosystems have recently received increasing attention from the carbon financing sector. This has sparked the need for reliable and non-destructive methods to estimate carbon stocks in these ecosystems. The puna grasslands of the high Andes represent such a system and the current study investigated species richness and carbon stocks (in above- and below ground biomass) at a puna site in Peru. The study also examined the effect of fire on species richness and carbon stocks by comparing burnt and unburnt areas. Species-specific allometric equations were developed for four grass species, and generalised grassland equations were developed,
combining data from both the burnt and unburnt area. No significant difference in carbon stocks between the burnt and unburnt area was found. The areas combined contained on average 3.4 Mg C ha-1 ± 0.1 SE stored in above-ground biomass, and 3.1 Mg C ha-1 ± 0.2 SE in below-ground biomass. Species richness was similar, but species composition differed somewhat between the burnt and unburnt area; the exotic species Juncus balticus was found mainly in the burnt area, and two Lycopodium species were found mainly in the unburnt area. However, Calamagrostis sp.
was the dominant grass species in both areas. Highly significant allometric models were developed for four grass species separately. A generalised model combining the four was also developed. Some of the species-specific equations were affected by fire history. These results suggest that carbon estimations using allometric equations in puna grasslands can be more accurate if the fire history of the study area is known. It also seems that puna grasslands can recover their carbon stocks within three years of burning. However, species composition is altered by fire and appears to need more time to revert to pre-fire structure.
Key words: allometric equations, carbon, fire ecology, functional ecology, grasslands, Manu, mountains, Peru, puna.
IV
Table of contents
Preface I
Abstract III
Introduction 1
Methods 2
Results 8
Discussion 21
Conclusion 25
References 27
1
Introduction
The Andean grasslands in Peru (puna) have been exposed to increasing anthropogenic pressures during the last decades, mainly from grazing and burning (Bustamente Becerra & Bitencourt 2007;
Tapia Nunez & Flores Ochoa 1984 in Bustamente Becerra & Bitencourt 2007). This could potentially lead to increased levels of soil erosion (Oscanoa 1988 in Bustamente Becerra &
Bitencourt 2007), and consequently a decline in vegetation cover, primary production (Fensham 1997), plant diversity (Bustamente Becerra 2006), seed production and the amount of seeds stored in soil (Bertiller 1996; Coffin & Lauenroth 1989). It is also believed that grazing and burning of the puna in forest-puna transition zones constrains the upper limit of the tree line (Braun et al. 2002;
Sarmiento & Frolich 2002; Young & León 2007). A serious concern considering that estimations for temperature rises during the next century may require species to migrate upwards at rates
significantly higher than during the last 50,000 years (Bush et al. 2004; Feeley & Silman 2010). A balance between upwards migration of forests and conservation of puna biodiversity needs to be found.
Another aspect of fire and grazing pressure is their implications for carbon stocks.
Anthropogenic land use is now widely considered to either contribute to carbon emissions through degrading land practices, or to function as a carbon sink for atmospheric carbon through
sequestration in below- and above-ground forest- and grassland components (Denman et al. 2007).
This has stimulated research on many different ecosystems with regards to global carbon dynamics, and their potential role in the recently developed carbon markets (e.g. Glenday 2006; Malhi &
Grace 2000). Reforestation, avoided deforestation and better grassland management are some of the ways carbon credits for the voluntary carbon market can be generated (Hamilton et al. 2009), and even though most of the work until now has focused on lowland forest ecosystems, increasing attention is now given to carbon dynamics at higher elevations with the increasing recognition that these ecosystems also could benefit from carbon financing (e.g. Fehse et al. 2002; Malhi et al.
2010).
The frequent burning of the puna grasslands is likely to represent considerable emissions of carbon to the atmosphere, but little is known about puna carbon dynamics, especially in relation to fire (e.g. fuel build up). In one of the few studies conducted in puna areas, Gibbon et al. (2010) found that more carbon was stored in the soil of puna sites unaffected by fire than those that were fire exposed. However, the relationship was not statistically significant (Gibbon et al. 2010). No difference in carbon stored in above-ground biomass in relation to fire exposure was found either (Gibbon et al. 2010). In short, information on carbon dynamics under different disturbance regimes in puna areas is very sparse. More research is therefore clearly needed on puna carbon dynamics in relation to land use practices, and methods for estimation of carbon stocks need to be developed in
2 relation to carbon trade.
Allometric equations have been shown to be an effective and non-destructive tool for estimating above ground biomass/carbon stocks (Chave et al. 2005; Litton & Kauffman 2008;
Nafus et al. 2009). These equations can be species specific (e.g. Litton & Kauffman 2008) or more generalized (e.g. Chave et al. 2005; Nafus et al. 2009). Most of the existing equations focus on trees, since forests have received most of the attention with regards to carbon dynamics. The recent increased recognition that other ecosystems, such as grasslands, also contribute significantly to the global carbon cycle due to human land use (Scurlock & Hall 1998; Schuman et al. 2002), has sparked some interest in the development of allometric equations for these areas (e.g. Guevara et al.
2002; Nafus et al. 2009). For grasslands, generalised, species- and ecosystem-specific equations for dominant grasses and herbs are needed if carbon stocks are to be estimated precisely in the future.
The aims of this project were (i) to explore and quantify differences in carbon stocks of above- and below-ground biomass in an area exposed to fire three years previously and an area protected from fire for several years, (ii) to explore how the two areas differed in species richness and species composition and (iii) to develop allometric equations for the dominant grass species in the area for non-destructive above-ground carbon stock estimation in the future.
Methods
Site Description
The Manu National Park stretches from the Peruvian Amazon lowlands to the eastern slopes of the Andean mountains (IUCN 2008). The 1.5 million ha park is situated between the catchment basins of the Urubamba and Madeira rivers to the south and west, and the catchment of the Manu river in the eastern lowlands (Fig. 1; IUCN 2008). With an altitude gradient stretching from about 350 masl in the lowlands, to grasslands at around 4,000 masl, the park contains an extremely high diversity of habitats and species (IUCN 2008). Manu National Park was added to the World Heritage List in 1987 (IUCN 2008).
The study was conducted near the Wayqecha research station in the Manu buffer zone in the south-western mountainous part of the reserve at approximately 3300 masl (approximate
coordinates 13o18´S, 71o58´W). The high altitude areas near Wayqecha have a typical puna vegetation type dominated mainly by tussock-forming grasses. Some of the dominant species are Jarava ichu Ruiz & Pav., Calamagrostis vicunarum (Wedd.) Pilg. and Festuca dolichophylla J.
Presl. (Gibbon et al. 2010). Average annual rainfall is 1900 to 2500 mm, with a wet season from October to April (Gibbon et al. 2010). Mean annual temperature is approximately 11oC (at 3600 m;
Gibbon et al. 2010). Puna soils are largely composed of an organic-rich A-layer, stony B/C-layers, and no Oh-layer (Gibbon et al. 2010; Zimmerman et al. 2009). Gibbon et al. (2010)
3
Figure 1: Map showing the location of the study area. The green border represents Manu National Park. The pink area represents the area of the Wayqecha Cloud Forest Research Centre, part of the southern buffer zone of Manu National Park.
reported a mean puna soil depth of 33 cm. The puna has been subject to high grazing and fire pressure over the years, and is classified as a “Zone of Recovery” by the Manu National Park, highlighting the need for spatial management for recovery (INRENA 2002 in Gibbon et al. 2010).
Above-ground sampling strategy
Eight transects of 30 m were set up (Fig. 2); four in an area burned in 2007 (Imma Oliveras pers.
comm.) and four in an area unaffected by fire for at least ten years (Imma Oliveras pers. comm.).
The sites are subject to similar grazing pressure. In each transect eight plots of 2 x 2 m were set up, each separated by two meters. All plants were identified to species level before the following measurements were taken for each tussock: The longest basal diameter and the longest perpendicular to the first (mm), the height as encountered in field (cm), the maximum height (stretched by hand; cm), the longest tussock crown diameter and the longest perpendicular to the first (cm). The crown- and basal diameters were averaged and used to estimate circular canopy areas and basal areas. The highest vegetative tiller was defined as plant height, excluding reproductive tillers that may surpass vegetative tillers. The biomass of these is negligible
(Cavagnaro et al. 1983 in Guevara et al. 2002). Tussock volume was derived from plant heights and basal diameters using the “Basal Elliptical Cylinder” method as recommended by Johnson et al.
4
(1988; Fig. 3). All plants were hand clipped at ground level. Following Ramsay & Oxley (2001), dead material still attached to the tussocks was harvested, but ground litter was not. All plants were bagged and subsequently oven dried at 70oC to constant weight, and weighed to the nearest 0.1 g.
Below-ground sampling strategy
In each transect, four soil cores 12 cm in diameter and 30 cm in depth were extracted using opposable semicircular cutting blades. Small portions of soil were extracted at a time to avoid soil compression. The extracted soil was separated into an organic rich organic layer (OL) and a mineral layer (ML) and homogenised. Roots were extracted from each layer during four ten minute time intervals using one small plastic bag for the roots extracted per time interval. The soil was returned to the ground in its original layering after sampling. Following Girardin et al. (2010), the roots were transported to the lab where they were washed to remove inorganic material, separated into coarse roots (> 2 mm diameter) and fine roots (< 2 mm diameter), and dried to constant weight before they were weighed to the nearest 0.01 grams.
Carbon estimation
Dried vegetative biomass was assumed to contain 50 % carbon (following e.g. Gibbon et al. 2010;
Glenday 2006).
Effect of fire on above-ground biomass and carbon stocks
Differences in total above-ground biomass between the burnt and unburnt area were compared using an independent samples t-test.
Effect of fire history on species richness and functional diversity
Plants in all plots were determined to species level and their biomass subsequently measured.
Differences in plant biomass for the different species between the burnt and unburnt area were compared using independent samples t-tests.
Statistical analyses for below-ground biomass
The curve of cumulative root extraction over time was used to estimate root biomass that could potentially be extracted beyond 40 minutes for each soil sample, as shown by Metcalfe et al. (2007).
This method corrects for the underestimation of below ground biomass often experienced in other
5
a b
c d
e f
Figure 2: Fieldwork images. a – setting up a transect. b – measuring a tussock. c – harvesting and marking a tussock.
d – weighing samples. e – Calamagrostis sp. tussock. f – a 2x2 meter square after sampling.
6
Figure 3: Canopy volume model calculated as a Basal Elliptical Cylinder using basal diameter and height measurements. Figure from Johnson et al. (1988).
methodologies (Metcalfe et al. 2007) and is much less time consuming without compromising measurement accuracy (Girardin et al. 2010; Metcalfe et al. 2007). The data obtained were used to estimate the amount of total biomass allocated below ground (in Mg/ha). The root biomass
estimations were carried out using Microsoft Excel for Windows (Microsoft Corporation, Redmond, WA, U.S.A.). Differences in total below-ground biomass between the burnt and the unburnt area were compared using an independent samples t-test.
Statistical analyses for above-ground biomass
Calamagrostis sp., Festuca dolichophylla, Scirpus rigidus and Juncus balticus have growth forms that make them suitable for developing allometric equations. These four species made up 84.9 % of the total biomass at the study site. The rest of the species have growth forms that make it difficult to explore allometric relationships with the methods used here, thus equations for these were not developed. Allometric equations were developed for the burnt and the unburnt area separately and for the two areas combined. A multispecies equation was also developed, using the data from both the burnt and unburnt area combined. The best models from the burnt and unburnt area were compared to determine if fire history affected the coefficients of the equations. If the 95 %
confidence intervals of the coefficients overlapped, they were considered not significantly different.
Because low numbers of Juncus balticus individuals were found, fire history specific equations were not developed for this species. All measured variables were log10 transformed in order to remove nonlinearity and heterogeneity of variance. Stepwise and simple regression was used to identify which variables influenced the model most and to identify possible co-linearity conflicts.
Based on visual analysis of scatter-plots of estimators vs. biomass, the most extreme outliers (most
7
likely annotation errors) were removed. However, the number of samples removed from the analysis was very low (<15).
Linear regression was performed to produce equations of the form Y = a + bX
where Y = the log transformed dependent variable (plant biomass in grams), X = a log transformed independent variable (tussock volume, crown area, height or basal area) and a, and b are the
regression coefficients derived from the linear regression analysis.
Some scatter-plots of independent variables vs. biomass suggested a more nonlinear tendency even after log10 transformation. Therefore, nonlinear regression was also performed to produce equations of the form
Y = aXb
where Y = the log transformed dependent variable (plant biomass in grams), X = a log transformed independent variable (tussock volume, crown area, height or basal area) and a, and b are the
regression coefficients derived from the nonlinear regression analysis.
Approximately 80 % of the data (called the estimation data set) were used to obtain the allometric relationships and 20 % (called the prediction data set) were used for validating the equations. Model accuracy was determined using the coefficient of determination (R2), and the standard error of the estimate (SEE) with a higher R2 and a lower SEE being a better fit than the opposite. Following e.g. Niklas (2006) analysis of residuals was also used. This was done through visual analysis of plots of predicted values against biomass residuals.
The addition of more than one independent variable to improve the equations was also explored, giving linear equations of the form
Y = a + bX1 +cX2
and
Y = a + bX1 + cX2 +dX3 ,
where Y = the log transformed dependent variable (plant biomass in grams), Xn = a log transformed independent variable (tussock volume, crown area, height or basal area) and a, b, c and d are the regression coefficients derived from the linear regression analysis.
More variables were also added to the nonlinear models, producing equations of the form Y = aX1b + cX2d
and
Y = aX1b + cX2d + eX3f
where Y = the log transformed dependent variable (plant biomass in grams), Xn = a log transformed
8
independent variable (tussock volume, crown area, height or basal area) and a, b, c, d, e and f are the regression coefficients derived from the nonlinear regression analysis.
Some authors note that nonlinear regression techniques with untransformed data have often been used in studies of grass allometry (e.g. Johnson et al. 1988). The log10 transformed approach is used here because the raw data were not normally distributed, and because the analysis of residuals after exploring both techniques suggested a better fit for the log10 transformation method.
All analyses were carried out using SPSS 17.0 for Windows (SPSS Inc., Chicago, IL, U.S.A.) unless otherwise specified.
Results
Effect of fire on above-ground biomass and carbon stocks
The unburnt area contained more above-ground biomass than the burnt area, but the difference was not significant (P=0.27). The above-ground vegetation in both areas combined was estimated to contain on average 6.7 Mg ha-1 ± 0.2 SE dry biomass, which translates to 3.4 Mg C ha-1 ± 0.1 SE.
Effect of fire on functional diversity
The number of species in the burnt and unburnt plots was very similar (34 and 32, respectively).
The species with the highest biomass was Calamagrostis sp. in both the burnt and unburnt area (Fig. 4). This species alone made up 71.5 % and 66.3 % of the total biomass in the burnt and unburnt area, respectively. However, there was no significant difference in Calamagrostis sp.
biomass between the areas (P=0.994). Further, Festuca dolichophylla and Scirpus rigidus had a relatively high biomass in both areas, with more of both being found in the unburnt area (Fig. 4).
However, these differences were not significant (P=0.162 and P=0.63 for Festuca dolichophylla and Scirpus rigidus, respectively).
The burnt area contained higher biomass of Juncus balticus (P=0.004), Baccharis pygmaea (P=0.004) and Blechnum sp. (not significant P=0.282; Fig. 4). More biomass of Senecio
rhizomatosus (P=0.003) and of two Lycopodium species was found in the unburnt than in the burnt area (one significant (P=0.035) and the other P=0.077; Fig. 4).
Effect of fire on below-ground biomass and carbon stocks
The unburnt area contained more below-ground biomass than the burnt area, but the difference was not significant (P=0.867). Few roots had diameters > 2 mm, and no roots were wider than ~ 4 mm.
All the roots found were therefore treated as fine root biomass. The puna below ground vegetation was estimated to contain on average 6.3 Mg ha-1 ± 0.4 SE dry biomass, which translates to 3.1 Mg C ha-1 ± 0.2 SE.
9
Figure 4: Mean biomass (grams per 2x2 meter plot) of a selection of species from a puna grassland, Peru. Blue bars indicate plants from an area protected from fire >10 years. Green bars indicate plants from an area burnt approximately three years before harvest. Error bars indicate 95 % confidence intervals of the mean. Asterisks indicate significant difference.
Allometric equations
Stepwise and simple regression techniques revealed that models based on basal area and height (either separately or as volume model) were good estimators of plant biomass. Basal area was the single most influential estimator, but adding height always improved the models. The addition of canopy area improved models in some cases, and in others not. The maximum height was a better estimator than height as encountered in field, and all models including height are therefore
performed using the maximum height data.
Species-specific, fire history independent equations for both the estimation and the
prediction datasets are presented in tables 1-4. Results for the burnt area are shown in tables 5-7 and for the unburnt area in tables 8-10. The comparison of coefficients based on the best fire history related models is presented in table 11. The results from the multispecies-multi area regressions are shown in table 12. All models had highly significant F-ratios (p < 0.001), and their residuals were determined to be approximately normally distributed.
10
Table 1: Linear and nonlinear regression equations of different log transformed data (tussock basal area in mm2 (X1), tussock volume in cm3 (X2), canopy area in cm2 (X3), maximum plant height in cm (X4)) on log transformed plant dry biomass in g for Calamagrostis sp., and comparison of estimation and prediction data statistics. Equations combine data from a burnt and an unburnt puna site. A higher R2 and a lower SEE (standard error of the estimate) is considered a better fit. n estimation set = 1085, n prediction set = 249.
Coefficient
Regression Estimator a b c d e f R2 SEE
Prediction SEE
Linear X1 -1.274 0.792 0.759 0.301 0.279
Nonlinear X1 0.091 2.196 0.794 0.277 0.268
Linear X2 -0.751 0.696 0.813 0.266 0.244
Nonlinear X2 0.195 1.706 0.835 0.248 0.23
Linear X2 X3 -1.606 0.463 0.544 0.854 0.235 0.219
Nonlinear X2 X3 0.257 1.529 -0.691 -1.9 0.838 0.246 0.23
Linear X1 X4 -2.787 0.626 1.195 0.827 0.256 0.234
Nonlinear X1 X4 0.242 1.587 -1.329 -2.703 0.818 0.26 0.244
Linear X1 X3 -2.162 0.461 0.692 0.841 0.245 0.232
Nonlinear X1 X3 0.202 1.695 -1.252 -1.578 0.805 0.27 0.258
Linear X1 X4 X3 -2.744 0.464 0.494 0.661 0.855 0.234 0.298
Nonlinear X1 X4 X3 0.266 1.526 -1.202 -2.775 -0.415 -1.732 0.819 0.26 0.244
Table 2: Linear and nonlinear regression equations of different log transformed data (tussock basal area in mm2 (X1), tussock volume in cm3 (X2), canopy area in cm2 (X3), maximum plant height in cm (X4)) on log transformed plant dry biomass in g for Scirpus rigidus, and comparison of estimation and prediction data statistics. Equations combine data from a burnt and an unburnt puna site. A higher R2 and a lower SEE (standard error of the estimate) is considered a better fit. n estimation set = 508, n prediction set = 130.
Coefficient
Regression Estimator a b c d e f R2 SEE
Prediction SEE
Linear X1 -0.745 0.554 0.675 0.287 0.319
Nonlinear X1 0.09 2.047 0.694 0.279 0.301
Linear X2 -0.46 0.534 0.775 0.239 0.266
Nonlinear X2 0.183 1.639 0.788 0.232 0.252
Linear X2 X3 -1.49 0.363 0.522 0.838 0.203 0.223
Nonlinear X2 X3 -93.919 -0.006 92.376 0.021 0.777 0.238 0.256
Linear X1 X4 -2.42 0.473 1.192 0.808 0.221 0.225
Nonlinear X1 X4 -341.264 -0.003 340.042 0.006 0.76 0.246 0.262
Linear X1 X3 -1.993 0.327 0.685 0.807 0.222 0.24
Nonlinear X1 X3 -2.474 -0.389 1.01 0.903 0.784 0.234 0.25
Linear X1 X4 X3 -2.603 0.359 0.432 0.762 0.843 0.2 0.502
Nonlinear X1 X4 X3 -416.124 -0.002 415.246 0.003 0.006 3.966 0.833 0.207 0.24
11
Table 3: Linear and nonlinear regression equations of different log transformed data (tussock basal area in mm2 (X1), tussock volume in cm3 (X2), canopy area in cm2 (X3), maximum plant height in cm (X4)) on log transformed plant dry biomass in g for Festuca dolichophylla, and comparison of estimation and prediction data statistics. Equations combine data from a burnt and an unburnt puna site. A higher R2 and a lower SEE (standard error of the estimate) is considered a better fit. n estimation set = 183, n prediction set = 40.
Coefficient
Regression Estimator a b c d e f R2 SEE
Prediction SEE
Linear X1 -0.802 0.66 0.747 0.253 0.392
Nonlinear X1 0.167 1.744 0.763 0.244 0.4
Linear X2 -0.566 0.623 0.782 0.235 0.342
Nonlinear X2 0.239 1.522 0.809 0.221 0.328
Linear X2 X3 -1.231 0.508 0.333 0.801 0.225 0.327
Nonlinear X2 X3 -308.246 -0.004 306.965 0.004 0.751 0.252 0.35
Linear X1 X4 -3.021 0.557 1.382 0.804 0.224 0.327
Nonlinear X1 X4 -213.656 -0.007 211.572 0.013 0.759 0.248 0.347
Linear X1 X3 -1.669 0.492 0.463 0.787 0.233 0.356
Nonlinear X1 X3 -167.114 -0.008 165.35 0.009 0.733 0.262 0.384
Linear X1 X4 X3 -3.094 0.476 0.286 1.094 0.816 0.217 1.054
Nonlinear X1 X4 X3 -265.389 -0.005 263.996 0.007 5.47E-005 7.194 0.815 0.219 0.363
Table 4: Linear and nonlinear regression equations of different log transformed data (tussock basal area in mm2 (X1), tussock volume in cm3 (X2), canopy area in cm2 (X3), maximum plant height in cm (X4)) on log transformed plant dry biomass in g for Juncus balticus, and comparison of estimation and prediction data statistics. Equations combine data from a burnt and an unburnt puna site. A higher R2 and a lower SEE (standard error of the estimate) is considered a better fit. n estimation set = 140, n prediction set = 37.
Coefficient
Regression Estimator a b c d e f R2 SEE
Prediction SEE
Linear X1 -0.641 0.488 0.665 0.289 0.311
Nonlinear X1 0.067 2.215 0.68 0.282 0.308
Linear X2 -0.361 0.475 0.743 0.254 0.266
Nonlinear X2 0.166 1.686 0.75 0.25 0.242
Linear X2 X3 -1.234 0.362 0.443 0.788 0.231 0.232
Nonlinear X2 X3 0.285 1.277 -2.333 -3.266 0.771 0.24 0.24
Linear X1 X4 -1.681 0.429 0.8 0.74 0.256 0.244
Nonlinear X1 X4 0.397 1.078 -0.847 -1.42 0.718 0.268 0.268
Linear X1 X3 -1.782 0.341 0.608 0.769 0.241 0.248
Nonlinear X1 X3 1.023 0.544 -2.993 -1.146 0.739 0.256 0.273
Linear X1 X4 X3 -1.982 0.349 0.466 0.359 0.778 0.237 0.248
Nonlinear X1 X4 X3 59.299 0.013 -16.726 -0.032 -44.009 -0.03 0.749 0.254 0.248
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Table 5: Linear and nonlinear regression equations of different log transformed data (tussock basal area in mm2 (X1), tussock volume in cm3 (X2), canopy area in cm2 (X3), maximum plant height in cm (X4)) on log transformed plant dry biomass in g for Calamagrostis sp., and comparison of estimation and prediction data statistics. Equations were developed with data from a puna site burned approximately three years before harvest. A higher R2 and a lower SEE (standard error of the estimate) is considered a better fit. n estimation set = 575, n prediction set = 130.
Coefficient
Regression Estimator a b c d e f R2 SEE
Prediction SEE
Linear X1 -1.196 0.773 0.746 0.317 0.291
Nonlinear X1 0.085 2.249 0.796 0.284 0.277
Linear X2 -0.681 0.685 0.811 0.274 0.242
Nonlinear X2 0.177 1.799 0.855 0.24 0.219
Linear X2 X3 -1.634 0.434 0.597 0.861 0.235 0.207
Nonlinear X2 X3 -0.809 -0.619 0.245 1.894 0.811 0.273 0.252
Linear X1 X4 -2.647 0.58 1.233 0.83 0.259 0.236
Nonlinear X1 X4 -272 -0.005 270.45 0.008 0.771 0.301 0.376
Linear X1 X3 -2.204 0.426 0.756 0.85 0.243 0.214
Nonlinear X1 X3 -1.468 -1.013 0.269 1.819 0.823 0.266 0.242
Linear X1 X4 X3 -2.636 0.428 0.543 0.609 0.862 0.233 0.219
Nonlinear X1 X4 X3 -372.855 -0.003 372.067 0.003 0.004 4.504 0.869 0.228 0.346
Table 6: Linear and nonlinear regression equations of different log transformed data (tussock basal area in mm2 (X1), tussock volume in cm3 (X2), canopy area in cm2 (X3), maximum plant height in cm (X4)) on log transformed plant dry biomass in g for Scirpus rigidus, and comparison of estimation and prediction data statistics. Equations were developed with data from a puna site burned approximately three years before harvest. A higher R2 and a lower SEE (standard error of the estimate) is considered a better fit. n estimation set = 192, n prediction set = 56.
Coefficient
Regression Estimator a b c d e f R2 SEE
Prediction SEE
Linear X1 -0.815 0.603 0.704 0.293 0.3
Nonlinear X1 0.096 2.055 0.728 0.282 0.298
Linear X2 -0.547 0.595 0.8 0.241 0.272
Nonlinear X2 0.18 1.727 0.821 0.228 0.275
Linear X2 X3 -1.691 0.411 0.567 0.862 0.2 0.214
Nonlinear X2 X3 -143.18 -0.005 141.376 0.015 0.816 0.232 0.234
Linear X1 X4 -2.721 0.513 1.356 0.849 0.209 0.268
Nonlinear X1 X4 -275.022 -0.005 273.559 0.008 0.814 0.232 0.291
Linear X1 X3 -2.237 0.369 0.743 0.837 0.218 0.214
Nonlinear X1 X3 -47.765 -0.019 45.448 0.048 0.817 0.232 0.223
Linear X1 X4 X3 -2.871 0.412 0.419 0.892 0.874 0.192 0.684
Nonlinear X1 X4 X3 -340.655 -0.003 339.437 0.004 0.021 2.971 0.859 0.204 0.216
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Table 7: Linear and nonlinear regression equations of different log transformed data (tussock basal area in mm2 (X1), tussock volume in cm3 (X2), canopy area in cm2 (X3), maximum plant height in cm (X4)) on log transformed plant dry biomass in g for Festuca dolichophylla, and comparison of estimation and prediction data statistics. Equations were developed with data from a puna site burned approximately three years before harvest. A higher R2 and a lower SEE (standard error of the estimate) is considered a better fit. n estimation set = 70, n prediction set = 15.
Coefficient
Regression Estimator a b c d e f R2 SEE
Prediction SEE
Linear X1 -0.869 0.701 0.758 0.251 0.154
Nonlinear X1 0.181 1.718 0.77 0.248 0.164
Linear X2 -0.57 0.645 0.785 0.236 0.167
Nonlinear X2 0.251 1.515 0.798 0.232 0.173
Linear X2 X3 -1.41 0.543 0.381 0.806 0.226 0.158
Nonlinear X2 X3 -185.043 -0.008 183.335 0.008 0.773 0.246 0.216
Linear X1 X4 -2.554 0.589 1.117 0.788 0.237 0.189
Nonlinear X1 X4 -200.191 -0.009 198.241 0.012 0.759 0.254 0.207
Linear X1 X3 -1.841 0.567 0.467 0.792 0.234 0.141
Nonlinear X1 X3 -146.252 -0.011 144.017 0.011 0.766 0.25 0.167
Linear X1 X4 X3 -2.803 0.52 0.354 0.79 0.805 0.229 0.641
Nonlinear X1 X4 X3 -75.375 -0.02 73.745 0.021 0.01 3.303 0.786 0.242 0.176
Table 8: Linear and nonlinear regression equations of different log transformed data (tussock basal area in mm2 (X1), tussock volume in cm3 (X2), canopy area in cm2 (X3), maximum plant height in cm (X4)) on log transformed plant dry biomass in g for Calamagrostis sp., and comparison of estimation and prediction data statistics. Equations were developed with data from a puna site protected from fire >10 years before harvest. A higher R2 and a lower SEE (standard error of the estimate) is considered a better fit. n estimation set = 514, n prediction set = 122.
Coefficient
Regression Estimator a b c d e f R2 SEE
Prediction SEE
Linear X1 -1.623 0.888 0.774 0.277 0.256
Nonlinear X1 0.094 2.17 0.79 0.268 0.244
Linear X2 -1.147 0.808 0.825 0.244 0.223
Nonlinear X2 0.16 1.855 0.84 0.234 0.212
Linear X2 X3 -1.871 0.554 0.522 0.861 0.218 0.221
Nonlinear X2 X3 0.305 1.45 -1.818 -1.922 0.849 0.228 0.219
Linear X1 X4 -3.655 0.703 1.506 0.836 0.237 0.225
Nonlinear X1 X4 0.455 1.25 -2.908 -2.49 0.827 0.242 0.236
Linear X1 X3 -2.361 0.533 0.666 0.841 0.232 0.238
Nonlinear X1 X3 0.706 1.002 -3.073 -1.051 0.816 0.25 0.254
Linear X1 X4 X3 -3.543 0.504 0.483 1.027 0.865 0.215 0.712
Nonlinear X1 X4 X3 50.665 0.032 -20.38 -0.098 -33.448 -0.043 0.841 0.234 0.248
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Table 9: Linear and nonlinear regression equations of different log transformed data (tussock basal area in mm2 (X1), tussock volume in cm3 (X2), canopy area in cm2 (X3), maximum plant height in cm (X4)) on log transformed plant dry biomass in g for Scirpus rigidus, and comparison of estimation and prediction data statistics. Equations were developed with data from a puna site protected from fire >10 years before harvest. A higher R2 and a lower SEE (standard error of the estimate) is considered a better fit. n estimation set = 318, n prediction set = 85.
Coefficient
Regression Estimator a b c d e f R2 SEE
Prediction SEE
Linear X1 -0.793 0.561 0.683 0.281 0.311
Nonlinear X1 0.077 2.156 0.715 0.268 0.296
Linear X2 -0.529 0.548 0.774 0.238 0.244
Nonlinear X2 0.148 1.803 0.803 0.223 0.232
Linear X2 X3 -1.447 0.374 0.486 0.826 0.209 0.204
Nonlinear X2 X3 -1.167 -0.569 0.332 1.519 0.773 0.238 0.232
Linear X1 X4 -2.427 0.473 1.176 0.809 0.219 0.207
Nonlinear X1 X4 -234.154 -0.005 232.819 0.008 0.767 0.242 0.248
Linear X1 X3 -1.918 0.329 0.646 0.798 0.225 0.228
Nonlinear X1 X3 -1.362 -0.95 0.204 1.851 0.775 0.238 0.236
Linear X1 X4 X3 -2.576 0.362 0.388 0.796 0.837 0.202 0.559
Nonlinear X1 X4 X3 -258.137 -0.003 257.3 0.004 0.001 5.385 0.842 0.2 0.221
Table 10: Linear and nonlinear regression equations of different log transformed data (tussock basal area in mm2 (X1), tussock volume in cm3 (X2), canopy area in cm2 (X3), maximum plant height in cm (X4)) on log transformed plant dry biomass in g for Festuca dolichophylla, and comparison of estimation and prediction data statistics. Equations were developed with data from a puna site protected from fire >10 years before harvest. A higher R2 and a lower SEE (standard error of the estimate) is considered a better fit. n estimation set = 110, n prediction set = 32.
Coefficient
Regression Estimator a b c d e f R2 SEE
Prediction SEE
Linear X1 -0.641 0.614 0.829 0.204 0.339
Nonlinear X1 0.204 1.589 0.834 0.202 0.337
Linear X2 -0.461 0.588 0.853 0.189 0.293
Nonlinear X2 0.259 1.451 0.86 0.187 0.282
Linear X2 X3 -0.652 0.548 0.104 0.855 0.189 0.279
Nonlinear X2 X3 0.267 1.431 -0.036 -0.929 0.86 0.187 0.282
Linear X1 X4 -2.834 0.538 1.309 0.861 0.185 0.244
Nonlinear X1 X4 0.371 1.213 -30.087 -8.106 0.862 0.184 0.258
Linear X1 X3 -0.967 0.538 0.188 0.836 0.2 0.309
Nonlinear X1 X3 0.286 1.384 -0.406 -1.039 0.836 0.202 0.328
Linear X1 X4 X3 -2.818 0.52 0.052 1.246 0.861 0.185 1.581
Nonlinear X1 X4 X3 0.134 1.749 -5.57 -3.351 0.904 0.065 0.869 0.181 0.234
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Table 11: Comparison of regression coefficients from similar regression models based on data from one area burned approximately 3 years before harvest and one area protected from fire >10 years. Regression models were derived from different log transformed data (tussock basal area in mm2 (X1), tussock volume in cm3 (X2), canopy area in cm2 (X3), maximum plant height in cm (X4)), with a higher R2 and a lower SEE (standard error of the estimate) considered a better fit. Models are considered different if compared coefficients lie outside each other's 95 % confidence intervals.
Coefficient
Species Area Regression Estimator a 95% interval b 95% interval c 95% interval R2 SEE Prediction SEE
Calamagrostis sp. Burnt Nonlinear X2 0.177 (0.159, 0.194) 1.799 (1.723, 1.875) 0.855 0.24 0.219
Unburnt Nonlinear X2 0.16 (0.143, 0.178) 1.855 (1.774, 1.937) 0.84 0.234 0.212
Burnt Linear X2 X3 -1.634 (-1.785, -1.483) 0.434 (0.393, 0.476) 0.597 (0.515, 0.678) 0.861 0.235 0.207
Unburnt Linear X2 X3 -1.871 (-2.031, -1.711) 0.554 (0.502, 0.607) 0.522 (0.432, 0.611) 0.861 0.218 0.221
Scirpus rigidus Burnt Nonlinear X2 0.18 (0.148, 0.212) 1.727 (1.578, 1.876) 0.821 0.228 0.275
Unburnt Nonlinear X2 0.148 (0.126, 0.170) 1.803 (1.679, 1.926) 0.803 0.223 0.232
Burnt Linear X2 X3 -1.691 (-1.954, -1.427) 0.411 (0.359, 0.464) 0.567 (0.447, 0.688) 0.862 0.2 0.214
Unburnt Linear X2 X3 -1.447 (-1.649, -1.245) 0.374 (0.328, 0.419) 0.486 (0.388, 0.584) 0.826 0.209 0.204
Festuca dolichophylla Burnt Nonlinear X2 0.251 (0.180, 0.322) 1.515 (1.292, 1.738) 0.798 0.232 0.173
Unburnt Nonlinear X2 0.259 (0.213, 0.304) 1.451 (1.311, 1.591) 0.86 0.187 0.282
Burnt Linear X2 X3 -1.41 (-2.085, -0.736) 0.543 (0.434, 0.652) 0.381 (0.098, 0.663) 0.806 0.226 0.158
Unburnt Linear X2 X3 -0.652 (-0.992, -0.313) 0.548 (0.468, 0.628) 0.104 (-0.062, 0.269) 0.855 0.189 0.279
Burnt Linear X1 X4 -2.554 (-3.694, -1.414) 0.589 (0.473, 0.705) 1.117 (0.390, 1.844) 0.788 0.237 0.189
Unburnt Linear X1 X4 -2.834 (-3.725, -1.943) 0.538 (0.481, 0.595) 1.309 (0.786, 1.833) 0.861 0.185 0.244
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Table 12: Linear and nonlinear regression equations of different log transformed data (tussock basal area in mm2 (X1), tussock volume in cm3 (X2), canopy area in cm2 (X3), maximum plant height in cm (X4)) on log transformed plant dry biomass in g for four puna grass species combined (Calamagrostis sp., Scirpus rigidus, Festuca dolichophylla and Juncus balticus), and comparison of estimation and prediction data statistics. Equations were developed from plants found both in a puna site protected from fire >10 years before harvest and from a site burned three years before harvest.
A higher R2 and a lower SEE (standard error of the estimate) is considered a better fit. n estimation data set = 1957, n prediction data set = 467.
Coefficient
Regression Estimator a b c d e f R2 SEE
Prediction SEE
Linear X1 -1.216 0.756 0.737 0.333 0.334
Nonlinear X1 0.072 2.339 0.779 0.306 0.317
Linear X2 -0.781 0.691 0.813 0.281 0.281
Nonlinear X2 0.147 1.912 0.851 0.25 0.258
Linear X2 X3 -1.61 0.509 0.472 0.845 0.256 0.25
Nonlinear X2 X3 0.167 1.824 -0.532 -2.658 0.852 0.25 0.258
Linear X1 X4 -2.881 0.584 1.309 0.834 0.264 0.26
Nonlinear X1 X4 0.281 1.483 -1.412 -2.407 0.817 0.279 0.281
Linear X1 X3 -2.263 0.477 0.676 0.817 0.278 0.273
Nonlinear X1 X3 0.16 1.826 -1.426 -1.88 0.789 0.298 0.308
Linear X1 X4 X3 -2.984 0.479 0.374 0.934 0.851 0.251 0.731
Nonlinear X1 X4 X3 0.286 1.47 -1.393 -2.412 -0.114 -2.221 0.817 0.279 0.279
Species-specific multi-area models
The linear model based on plant volume and canopy area gave the best fit for Calamagrostis sp..
However, when the predicted values were plotted against biomass residuals for this model, it seems that it underestimated biomass of small plants (Fig. 5). The nonlinear models based on volume and volume + canopy area also gave good fits, and give a better prediction for the full range of plant sizes (Fig. 6). These are therefore considered better than the linear model for Calamagrostis sp..
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Figure 5: Plot of predicted values vs. biomass residuals for a linear allometric model based on volume and canopy area for Calamagrostis sp. in a puna grassland, Peru. The model is based on data from an area burned approximately 3 years before harvest and an area protected from fire >10 years combined.
Figure 6: Plot of predicted values vs. biomass residuals for a nonlinear allometric model based on tussock volume for Calamagrostis sp. in a puna grassland, Peru. The model is based on data from an area burned approximately 3 years before harvest and an area protected from fire >10 years combined.
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Figure 7: Plot of predicted values vs. biomass residuals for a linear allometric model based on volume and canopy area for Scirpus rigidus in a puna grassland, Peru. The model is based on data from an area burned approximately 3 years before harvest and an area protected from fire >10 years combined.
Figure 8: Plot of predicted values vs. biomass residuals for a nonlinear allometric model based on volume for Festuca dolichophylla in a puna grassland, Peru. The model is based on data from an area burned approximately 3 years before harvest and an area protected from fire >10 years combined.
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Figure 9: Plot of predicted values vs. biomass residuals for a linear allometric model based on volume and canopy area for Juncus balticus in a puna grassland, Peru. The model is based on data from an area burned approximately 3 years before harvest and an area protected from fire >10 years combined.
A linear model based on volume and canopy area gave the best fit for Scirpus rigidus. The plot of predicted values vs. biomass residuals shows that it gives a balanced estimation for the full range of plant sizes (Fig. 7).
The Festuca dolichophylla analysis showed good results for nonlinear models based on volume alone and for volume combined with canopy area. Plots of predicted values vs. residuals were good for both models. However, the prediction data fit was considerably better for the model based on volume alone, and this model is therefore considered better (Fig. 8).
The analysis of Juncus balticus showed that a linear model combining volume and canopy area was the best fit. The plot of predicted values vs. biomass residuals was also balanced (Fig. 9).
Multispecies model
The multispecies analysis based on data from Calamagrostis sp., Scirpus rigidus, Festuca dolichophylla and Juncus balticus data from the burnt and unburnt area combined, showed that nonlinear models based on volume and volume + canopy area gave the best fits. The residual analysis from the model based on volume also show a balanced estimation over the full range of plant sizes (Fig. 10). Adding canopy area only improves the R2 value with 0.001(Table 12).
